JEE Advanced Physics 10 Years Topicwise Questions with Solutions
®
ERRORS
1. In an experiment for determination of the focal length of a thin convex lens, the distance of the object
from the lens is 10 ± 0.1 cm and the distance of its real image from the lens is 20 ± 0.2 cm. The error in
the determination of focal length of the lens is n %. The value of n is _______.
[JEE(Advanced) 2023]
2. Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is
0.5 mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale
shifts by two divisions. The measured readings are listed below. [JEE(Advanced) 2022]
Measurement condition Main scale reading Circular scale reading
Two arms of gauge touching 0 division 4 division
each other without wire
Attempt-1: With wire 4 divisions 20 divisions
Attempt-2: With wire 4 divisions 16 divisions
What are the diameter and cross-sectional area of the wire measured using the screw gauge?
(A) 2.22 ± 0.02 mm, π(1.23 ± 0.02) mm2 (B) 2.22 ± 0.01 mm, π(1.23 ± 0.01) mm
2
(C) 2.14 ± 0.02 mm, π(1.14 ± 0.02) mm2 (D) 2.14 ± 0.01 mm, π(1.14 ± 0.01) mm2
3. The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale
correspond to nine divisions of the main scale. The figure below on the left shows the reading of this
calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere
held between the jaws. The correct diameter of the sphere is [JEE(Advanced) 2021]
0 main scale 1 3 main scale 4
0 Vernier scale 10 0 Vernier scale 10
(A) 3.07 cm (B) 3.11 cm (C) 3.15 cm (D) 3.17 cm
4. Two capacitors with capacitance values C1 = 2000 ± 10 pF and C2 = 3000 ± 15 pF are connected in series.
The voltage applied across this combination is V = 5.00 ± 0.02 V. The percentage error in the calculation
of the energy stored in this combination of capacitors is _______. [JEE(Advanced) 2020]
5. An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal
length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm
mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at
135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens
is________. [JEE(Advanced) 2019]
1
, JEE Advanced Physics 10 Years Topicwise Questions with Solutions ®
Paragraph for Q.6 & Q.7
If the measurement errors in all the independent quantities are known, then it is possible to determine the
error in any dependent quantity. This is done by the use of series expansion and truncating the expansion
at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are
∆x, ∆y and ∆z, respectively, then
−1
x ± ∆x x ∆x ∆y
z ± ∆z = = 1 ± 1± .
y ± ∆y y x y
−1
∆y
The series expansion for 1 ± , to first power in ∆y/y, is 1 ( ∆y / y ) . The relative errors in
y
∆x ∆y
independent variables are always added. So the error in z will be =
∆z z + .
x y
∆x ∆y
The above derivation makes the assumption that << 1, << 1 . Therefore, the higher powers of these
x y
quantities are neglected.
(1 − a )
6. Consider the ratio r = to be determined by measuring a dimensionless quantity a. If the error in the
(1 + a )
measurement of a is ∆a(∆a/a << 1), then what is the error ∆r in determining r ? [JEE(Advanced) 2018]
∆a 2 ∆a 2 ∆a 2a∆a
(A) (B) (C) (D)
(1 + a ) 2
(1 + a ) 2
(1 − a )
2 (1 − a 2 )
7. In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed
in the first 1.0 s. For x << 1 , In (1 + x) = x up to first power in x. The error ∆λ, in the determination of
–1
the decay constant λ, in s is :- [JEE(Advanced) 2018]
(A) 0.04 (B) 0.03 (C) 0.02 (D) 0.01
8. A steel wire of diameter 0.5 mm and Young's modulus 2 × 1011 N m–2 carries a load of mass M. The
length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this
wire. Next to the steel wire is a reference wire to which a main scale, of least count
1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale.
Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is
increased by 1.2 kg, the vernier scale division which coincides with a main scale division is_______.
(Take g = 10 ms–2 and π = 3.2) [JEE(Advanced) 2018]
9. A person measures the depth of a well by measuring the time interval between dropping a stone and
receiving the sound of impact with the bottom of the well. The error in his measurement of time is
δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration due to
gravity g = 10 ms–2 and the velocity of sound is 300 ms–1. Then the fractional error in the measurement,
δL/L, is closest to [JEE(Advanced) 2017]
(A) 0.2% (B) 5% (C) 3% (D) 1%
2
JEE Advanced Physics 10 Years Topicwise Questions with Solutions
®
ERRORS
1. In an experiment for determination of the focal length of a thin convex lens, the distance of the object
from the lens is 10 ± 0.1 cm and the distance of its real image from the lens is 20 ± 0.2 cm. The error in
the determination of focal length of the lens is n %. The value of n is _______.
[JEE(Advanced) 2023]
2. Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is
0.5 mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale
shifts by two divisions. The measured readings are listed below. [JEE(Advanced) 2022]
Measurement condition Main scale reading Circular scale reading
Two arms of gauge touching 0 division 4 division
each other without wire
Attempt-1: With wire 4 divisions 20 divisions
Attempt-2: With wire 4 divisions 16 divisions
What are the diameter and cross-sectional area of the wire measured using the screw gauge?
(A) 2.22 ± 0.02 mm, π(1.23 ± 0.02) mm2 (B) 2.22 ± 0.01 mm, π(1.23 ± 0.01) mm
2
(C) 2.14 ± 0.02 mm, π(1.14 ± 0.02) mm2 (D) 2.14 ± 0.01 mm, π(1.14 ± 0.01) mm2
3. The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale
correspond to nine divisions of the main scale. The figure below on the left shows the reading of this
calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere
held between the jaws. The correct diameter of the sphere is [JEE(Advanced) 2021]
0 main scale 1 3 main scale 4
0 Vernier scale 10 0 Vernier scale 10
(A) 3.07 cm (B) 3.11 cm (C) 3.15 cm (D) 3.17 cm
4. Two capacitors with capacitance values C1 = 2000 ± 10 pF and C2 = 3000 ± 15 pF are connected in series.
The voltage applied across this combination is V = 5.00 ± 0.02 V. The percentage error in the calculation
of the energy stored in this combination of capacitors is _______. [JEE(Advanced) 2020]
5. An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal
length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm
mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at
135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens
is________. [JEE(Advanced) 2019]
1
, JEE Advanced Physics 10 Years Topicwise Questions with Solutions ®
Paragraph for Q.6 & Q.7
If the measurement errors in all the independent quantities are known, then it is possible to determine the
error in any dependent quantity. This is done by the use of series expansion and truncating the expansion
at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are
∆x, ∆y and ∆z, respectively, then
−1
x ± ∆x x ∆x ∆y
z ± ∆z = = 1 ± 1± .
y ± ∆y y x y
−1
∆y
The series expansion for 1 ± , to first power in ∆y/y, is 1 ( ∆y / y ) . The relative errors in
y
∆x ∆y
independent variables are always added. So the error in z will be =
∆z z + .
x y
∆x ∆y
The above derivation makes the assumption that << 1, << 1 . Therefore, the higher powers of these
x y
quantities are neglected.
(1 − a )
6. Consider the ratio r = to be determined by measuring a dimensionless quantity a. If the error in the
(1 + a )
measurement of a is ∆a(∆a/a << 1), then what is the error ∆r in determining r ? [JEE(Advanced) 2018]
∆a 2 ∆a 2 ∆a 2a∆a
(A) (B) (C) (D)
(1 + a ) 2
(1 + a ) 2
(1 − a )
2 (1 − a 2 )
7. In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed
in the first 1.0 s. For x << 1 , In (1 + x) = x up to first power in x. The error ∆λ, in the determination of
–1
the decay constant λ, in s is :- [JEE(Advanced) 2018]
(A) 0.04 (B) 0.03 (C) 0.02 (D) 0.01
8. A steel wire of diameter 0.5 mm and Young's modulus 2 × 1011 N m–2 carries a load of mass M. The
length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this
wire. Next to the steel wire is a reference wire to which a main scale, of least count
1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale.
Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is
increased by 1.2 kg, the vernier scale division which coincides with a main scale division is_______.
(Take g = 10 ms–2 and π = 3.2) [JEE(Advanced) 2018]
9. A person measures the depth of a well by measuring the time interval between dropping a stone and
receiving the sound of impact with the bottom of the well. The error in his measurement of time is
δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration due to
gravity g = 10 ms–2 and the velocity of sound is 300 ms–1. Then the fractional error in the measurement,
δL/L, is closest to [JEE(Advanced) 2017]
(A) 0.2% (B) 5% (C) 3% (D) 1%
2
